Comparison between the extracted NRFs () using matrix and MPM (reprinted from  with permission from IEEE).
Reliable radar target recognition has long been the holy grail of electromagnetic sensors. Target recognition based on the singularity expansion method (SEM) uses a time-domain electromagnetic signature and has been well studied over the last few decades. The SEM describes the late time period of the transient target signature as a sum of damped exponentials with natural resonant frequencies (NRFs). The aspect-independent and purely target geometry and material-dependent nature of the NRF set make it an excellent feature set for target characterization. In this chapter, we aim to review the background and the state of the art of resonance-based target recognition. The theoretical framework of SEM is introduced, followed by signal processing techniques that retrieve the target-dependent NRFs embedded in the transient electromagnetic target signatures. The extinction pulse, a well-known target recognition technique, is discussed. This chapter covers recent developments in using a polarimetric signature for target recognition, as well as using NRFs for subsurface sensing applications. The chapter concludes with some highlights of the ongoing challenges in the field.
- radar target recognition
- ultra wideband radar
- transient electromagnetic scattering
- singularity expansion method
The need to quickly and accurately identify enemies in confrontational situations is essential to most defense applications. Such decisions often rely upon radar target recognition. The two primary functions of radar are inherent in the acronym, whose letters stand for radio detection and ranging. There are two main categories of radar target recognition techniques: imaging and what is termed signature recognition. Imaging radars provide a visualization of the target using techniques such as focus spot scanning and inverse synthetic aperture . Signature recognition radar extracts some characteristics or a feature set that characterizes the target. Some of the techniques, such as radar cross section (RCS) , polarization techniques , high-resolution range profiles (HRRP) , scattering centers , and multiple frequency measurements , are all under this category. The main drawback of these techniques is that the extracted parameters usually vary with incident aspect. For most radar target recognition problems, usually, the incident aspect angles of the target are not known a priori. It is, therefore, preferable to implement a technique that is purely dependent on the target itself and independent of its aspect to the radar.
One of the methods that overcome the aspet-dependent limitation is termed resonance-based target recognition . As the name states, resonance-based target recognition essentially characterizes the radar target based on the natural resonant frequencies (NRFs) embedded in the target response. These NRFs are purely dependent on the physical attributes of the radar target, i.e., its dielectric properties and physical geometry, and these parameters are independent on the incident aspect  and incident polarization states . Provided of course the resonances are well excited, the feasibility of using the NRFs for target recognition has been successfully demonstrated in the literature [9, 10, 11].
This chapter aims to provide an overview of the fundamentals and the development of resonance-based target recognition. We commence the chapter with a short discussion on RCS—a well-known frequency-domain method on how electromagnetic scattering is characterized at microwave frequencies. The singularity expansion method (SEM), which is the theoretical framework for resonance-based target recognition, provides the physical description of the transient scattering phenomena in time and frequency domains. Technical solutions for retrieving the target-dependent NRFs from the transient target signatures and automated target recognition (ATR) algorithms will be covered. The recent development including the prospect of using full polarimetric signatures, as well as the potential use of the techniques in other sensing applications, is also discussed. Comments and suggestions for future development are considered in conclusion.
2. Resonance-based target recognition
RCS is a well-known technique to characterize target from 3 MHz up to 300 MHz (HF to mm) . Attempts have also been made to perform RCS measurement in the terahertz frequency region [12, 13]. RCS is a measure of the power that is returned or scattered in a given direction, normalized with respect to the power of the incident field. Mathematically, the RCS () of a target is defined as 
where is the range from the radar to the target and and are the amplitudes of the incident electric field from the radar transmitter and the scattered electric field from the target, respectively. The scattered field and thus the RCS of a definitive target, in general, vary as a function of incident aspects, receiving aspects, and excitation frequency. In the resonant regime which the wavelength of illumination () and the target size () are comparable (), every part of the target affects every other parts. The total field of any part of the target is the vectorial sum of the incident and scattered field due to every part of the scattering body. This collective interaction determines the overall electromagnetic current induced on the target, which explains why the induced current at resonant frequencies is dependent on the physical attributes of the target.
Resonance-based target recognition is based on the resonating electromagnetic current induced on the target such that the ratio of excitation wavelength () and the target size () has to be within the resonance scattering regime. The induced current serves as a secondary source and reradiates such that the resonant modes are embedded in the scattered target response. Rather than a frequency-domain characterization using RCS, one can also illuminate the target at a particular aspect in the time domain through a short-pulse excitation, measure the corresponding transient response at the same position (monostatic) or any another aspect (bistatic), and obtain the impulse response of the target. If one applies a Fourier transform to the target impulse response, this is the same as obtaining the frequency-domain “transfer function” of the target, thus evaluating the frequency dependency of the RCS at a particular transmit-receive configuration. Indeed, we assume that the bandwidth of the pulse is wide enough such that it covers at least the first few dominant resonant frequencies of the target.
2.1. Singularity expansion method
In the context of linear time-invariant (LTI) systems, the impulse response characterizes the behavior of the system and circuit. In the mid-1960s, Kennaugh and Moffatt  extended the concept of the impulse response and applied it to transient electromagnetic scattering from definitive targets. In the early 1970s, Baum  introduced the SEM that describes transient scattering phenomena. According to SEM, the entire transient target signature can be divided into two parts, namely, the early time and the late time period. Conceptually, the early time period is defined as the period from when the electromagnetic pulse initially strikes the target until the target is fully illuminated, while the commencement of the late time period is the time when global resonance has been fully established and the excitation is no longer present.
In the early time, the target is partly illuminated such that the majority of the scattering events originate locally from different parts of the target: specular reflections, diffraction from non-planar surfaces, edges, and corners. The occurrence of these events depends on when the pulse strikes on these edges and corners, and thus these early events are local, aspect dependent, and polarization dependent. They can be individually treated as scattering centers  or more generally using a wavefront description . In the time domain, these scattering events correspond to impulse-like components, and they are time-varying (nonstationary) and can be modeled in a circuit context using an entire function [7, 16, 17].
In contrast, the commencement of the late time period is the time when the target is fully illuminated such that resonant modes at distinct frequencies are fully established. As previously mentioned the total field at any part of the target is a collective interaction of the incident and scattered field from every single part of the target. At particular frequencies, the induced current on the target is freely resonating, and resonant modes are established. These resonant modes, known as natural resonance frequencies (NRFs), are theoretically dependent only on the physical attributes of the target and are independent of the aspect  and polarization . This allows them to be an excellent candidate to be used as a feature set for target classification. Mathematically, the late time target signature can be modeled as a sum of damped exponentials with constant residues, i.e.,
2.2. Resonance extractions for target classification
Target classification and recognition rely on accurate extraction of the target-dependent NRFs. There are two main approaches to extract these NRFs. The first one is based on the mathematical formulation of the scattering problem. Through a Fourier transform, the short-pulse excitation corresponds to a broadband of frequencies in the frequency domain. If we formulate the entire scattering problem at a particular frequency via an integral equation formulation, the integral equation relationship can be written in a matrix form and solved via moment methods . In general, this can be written as
where is an impedance-like matrix corresponding to the target geometry and and are column vectors corresponding to the unknown current induced on the target and the excitation, respectively. The natural resonant modes of the target, , are those such that the homogenous version of Eq. (3) has a nontrivial solution. This implies that the solution exists when the determinant of the matrix equals zero, thus establishing the singularities of the matrix. These singularities can be extracted using a typical (complex) root searching method such as Muller’s method . The matrix is constructed based solely on the geometry and dielectric properties of the target. The NRFs are therefore totally independent of the incident aspect angle. A major limitation is that the entire physical problem needs to be modeled using moment method, and each corresponds to only one frequency. This means that one needs to repeat the entire root searching process for all the frequency points, which requires extensive computation. Another limitation is that this method cannot be applied directly to measured data.
Shortly after the proposition of SEM by Baum, Van Blaricum and Mittra  proposed using Prony’s method which directly retrieves the NRFs and residues from the late time response in a computationally affordable manner. Prony’s method addresses the above limitations, and it has drawn significant attention in the field. However, the primary drawback of Prony’s method is that the accuracies of the extracted parameters are highly sensitive to noise and the estimated modal order of the signal. Since then, many techniques have been proposed which can accurately retrieve the modal order, NRFs, and residues with noisy target signatures. To date, direct extraction of NRFs from late time target signature has become the principal approach in this context, and matrix pencil methods (MPM) developed by Sarkar and Pereira  have become the main tool for this purpose.
To illustrate how NRFs can be used for target classification, as well as the aspect dependency nature of the resides, an example of a 1 m wire target illuminated under different excitation aspect angles shown in Figure 1 is considered . The wire target of length () and radius () ratio is excited by a plane wave with the electric field in the plane of the wire. The transient target responses are obtained using the indirect time-domain method —the scattering problem is first solved in the frequency domain at a large number of discrete frequency points, followed by Gaussian windowing to model a Gaussian pulse excitation  and an inverse Fourier transform. Here, the electromagnetic problem is solved using the moment method solver FEKO  from 4.39 MHz to 9 GHz with 2048 equally spaced samples. Given the target and incident aspect angles to the target, the late time can be approximated by
where is the maximal transit time of the target, is the effective pulse duration, and is the estimated edge when the pulse strikes the leading edge of the target . The Gaussian pulse commences at with . According to the geometry of Figure 1, where , and the excitation angles of are considered, resulting in , respectively. The NRFs are extracted using the MPM  with late time samples from 17 to 140 ns. The first ten dominant extracted NRFs are listed in Table 1 and are compared with the ground truth—NRFs extracted using a root searching procedure of the matrix .
The results show that all the first ten dominant resonant modes can be extracted only at , while some modes cannot be retrieved at and . To investigate of what is happening as the incidence angle varies, we transform the transient signatures to the joint time-frequency (TF) domain such that the existence and occurrences of the NRFs and scattering phenomena are clearly observed. Of all the time-frequency distributions (TFDs) in the Cohen class and the reassigned TFDs [26, 27], the Smooth Pseudo Wigner-Ville Distribution (SPWVD) gives reasonable TF resolutions without introducing uninterpretable artifacts [28, 29, 30].
The SPWVD, together with the corresponding time and frequency responses of the three signals, is shown in Figure 2(a)–(c). At , all the ten modes are identified in the joint TF domain. In Figure 2(b), modes 1 to 5 and mode 9 are observed when the incident angle is changed to . Mode 6 is not observed due to its small residue. Two resonant modes at about 1.2 and 1.5 GHz are also found in the figure. They have similar frequencies to modes 8 and 10 but with higher damping factors (marked with ^ in Table 1), which could probably be the higher layer NRFs . As the incident angle changes to , only modes 1 to 4, 6, 7, and 9 are excited, and they are be found correspondingly to those frequencies in Figure 2(c). In addition to the TF results, the NRFs also appear as peaks in the frequency response. As shown in both TF and frequency domains, it is apparent that the strength of the resonant modes, i.e., the residues, changes as the incident aspect varies, which validates the aspect dependency nature of the residues.
2.3. Extinction pulse technique
The target-dependent nature of the NRFs implies that the NRF patterns appearing in the S-plane are unique for a given target. Target recognition can thus be easily achieved by visually inspecting the patterns of the NRFs in the S-plane . To automate the identification procedure, Rothwell [9, 10, 11] proposed that target recognition can be performed by convolving the target signatures with a special type of filter, known as the “extinction pulse” or the “E-pulse,” in the time domain. The E-pulse is specially designed such that it will annul all the NRFs embedded in the late time response only if it is convolved with the response from the “true target.” Mathematically, the E-pulse, , can be defined as [9, 10, 11]
where is the late time target signature defined in Eq. (2), is the commencement of the late time period, and is the duration of .
To illustrate how E-pulse operates, an ATR scenario is shown in Figure 3 . The goal here is to identify the target given a measured target signature from an unknown target . In the target library, a number of E-pulses corresponding to different targets are stored. To perform ATR, is convolved with each of the E-pulses independently. According to Eq. (5), the one with a null response or smallest signal strength corresponds to the “true” target. Target identification is thus performed by monitoring the output of the convolution and picks up the one with the small energy level. To automate the process, the output is quantified using E-pulse discrimination number, , and the E-pulse discrimination ratio, , which are defined as follows :
Therefore, the target signature yielding the smallest and 0 dB is the one corresponding to the target of interest. This forms the basis for E-pulse ATR.
In most of our studies, we know a priori which one is the “right” target, and our goal is to determine if E-pulse is capable of discriminating the targets in new applications; for instance, the “banded” E-pulse technique that better discriminates between similar targets , a novel technique for subsurface target detection , and ATR using polarimetric signatures (Section 3.1). Figure 4 shows the flowchart of how we validate the E-pulse technique. For the case of three targets, there are three target signatures and three E-pulses, resulting in nine convolutions. Instead of using and in Eqs. (6) and (7), we modify them and introduce and discrimination ratio, , to quantify and convolution outcome and discrimination performance. They are given as follows [33, 35]:
is the case when the E-pulse and target response are from the same target, while is the case which the E-pulse and target returns are from different targets. A positive value of implies that is greater than and thus a successful target recognition. As we have a priori knowledge of correct targets, positive values are simply a validation of the success of E-pulse ATR or detection in the aforementioned new applications.
In practice, the E-pulse of a target can be obtained by numerically solving the convolution integral in Eq. (5) given the target signature  or using the formulation in  given the NRFs of the target. The E-pulses used in our studies (e.g., [33, 34, 35]) are constructed using the formulation in  together with the NRFs extracted from MPM.
3. Recent developments
Upon the introduction of SEM in the 1970s until the mid-1990s, research has mainly concentrated on three directions: theoretical studies with better modeling and description of early time scattering phenomena [15, 16], signal processing solutions to better retrieve SEM parameters for target characterization [17, 19, 20, 36, 37, 38, 39], and development of E-pulse and other ATR solutions for target recognition [11, 33, 40, 41, 42, 43, 44]. Most studies focused on ATR for targets in free space. The E-pulse proposed by Rothwell et al. [9, 10, 11, 36, 42] and the MPM algorithm by Sarkar and Pereira  have become the benchmark for filter-based ATR techniques and NRF extraction in this context. Since the 2000s, research activities have shifted toward applying the techniques developed in resonance-based target recognition for different applications. These include subsurface target detection, nondestructive evaluation, and medical diagnosis. Instead of using the linearly polarized electromagnetic wave to excite the target, the prospect of using fully polarimetric target signatures for ATR has also been investigated.
In this section, we first discuss the use of full polarimetric measurement and its impact on resonance-based target recognition. The merit of using polarimetric transient signatures is demonstrated through numerical examples. Then, different strategies for handling the
3.1. ATR using polarimetric signatures
The aspect dependency, as demonstrated in the above wire scattering example, as well as the polarization dependency of the residues, would limit the reliability and performance of ATR as it is uncertain whether all the dominant NRFs are well excited because the target orientation is usually not known a priori. In the mid-2000s, Shuley et al.  studied the residues retrieved from a target at 18 linear polarization angles at the same aspect and found that the residues of some NRFs could be so small at some polarization angles such that these NRFs are not retrieved. This was the first instance where polarization dependency of the residues is demonstrated. If we evaluate the RCS of the target at the resonant frequencies, the amplitudes of the scattered field, in general, vary as the observation aspects and polarization. This explains the aspect and polarization dependencies of the residues.
To accurately characterize a target using NRFs extracted from measured target signatures, it is important to incorporate more than one target signature obtained from different aspects and polarization states. Lui and Shuley  investigated different ways to process target signatures obtained from a number of polarization angles at a single aspect. Our results show that using the modified MPM  that allows extraction of one set of NRFs from multiple target signatures is preferred as it does not corrupt the original time-domain information and the risk of ignoring dominant modes is eliminated . The major drawback is that the computational load grows as the number of target signatures (aspects and polarization angles) is increased. Also, when linear polarization is used, it is not trivial to decide how many polarization angles are sufficient. To better understand the impact of using the different polarimetric response for ATR, examples of some simple wire targets will first be presented. Then, different ways to handle data set obtained from
In polarimetry, the Sinclair scattering matrices  in the linear and circular polarization bases are given by
Here, the subscripts denote the polarization channels (sets of transmit-receive polarization), where
To investigate the impact of the excitation and receiving states to the performance of ATR, numerical examples of three wire targets shown in Figure 5 were studied . The targets are made up of two wire segments—a vertical wire segment (main body) of 1 m and a horizontal wire segment of 0.3 m (Target 1 and Target 3) and 0.2 m (Target 2) located at the center (Target 1 and Target 2) and at 0.2 m away from the end of the main body (Target 3), respectively. The scattering problems of these targets are solved in the frequency domain using FEKO  with 512 equally spaced frequency samples from 3.9 MHz to 2 GHz. The polarimetric transient signatures, or equivalently the scattering matrices in the time domain, i.e.,
are determined using the aforementioned indirect time-domain method . For each target, the NRFs from each target signature is extracted using MPM  resulting eight sets of NRFs and residues. At each polarization state, the E-pulses for each of the three targets (denoted as target
Under vertical excitation, the main body is excited but not the horizontal wire segment. Theoretically, the cross polarized response should be zero in this case and vice versa for horizontal polarization excitation, and thus we only consider the co-polarized components. As tabulated in Table 2, the E-pulse technique fails to recognize between Target 1 and Target 2 for the case of , with and values near to 0 dB as only the NRFs corresponding to the main body are excited. For the case of , the horizontal wire segments of the two targets are well excited, and and values of 46.6 and 126.2 dB are obtained, which indicates successful target recognition. However, almost 0 dB of and values result. This is because the length of the horizontal wire segment of Target 1 and Target 3 is identical and the transient responses are strongly dominated by the horizontal wire segments. Under vertical polarization, the current distributions of the two targets are different due to different positions of the horizontal wire segments. The and values of 42.9 and 65.4 dB result which indicate the E-pulses successfully distinguish between Target 1 and Target 3. With different positions and length of the horizontal wire segments, the E-pulse is capable of distinguishing between Target 2 and Target 3 for both and . Under monostatic configuration and circularly polarized illumination, and , and thus we only need to consider and . values () of at least 26 dB result in all cases. Such results indicate that using circularly polarized target signatures can successfully discriminate the three targets.
In this example, ATR performance under different polarization states is studied. When the target is illuminated under linear polarization, only the main body or the horizontal wire segment is excited (details of the extracted NRFs can be found in ). The E-pulses are constructed using the incomplete set of NRFs. The target is poorly characterized and is not fully illuminated—these are the two main causes of the inconsistency in ATR performance. An example of the inconsistency in ATR performance due to aspect dependencies of the NRFs is reported in . When the target is illuminated under circular polarization, the NRFs of both wire segments are adequately excited. The constructed E-pulse contains the domain NRFs of the entire target. The target is well characterized and well illuminated under circular polarization. The consistent ATR performance originates from the fact that the NRFs of both wire segments of the targets are well excited. The findings from this example demonstrated the importance of including all the dominant NRFs (including both the global and partial/substructure resonances ) for target classification, as well as the importance of exciting all the dominant NRFs, especially when a library of similar targets is considered .
3.2. Target classification using
multiple-aspect multiple-polarization data set
Owing to the aspect and polarization dependencies of the residues, it is unlikely that the entire set of dominant NRFs can be excited from only one target signature. As shown above, target signatures obtained from different aspects and polarization states excite a different subset of dominant NRFs. Certainly, the use of multiple target signatures obtained from multiple aspect and polarization states for target characterization allows us to retrieve at least a larger subset of dominant NRFs within the frequency bandwidth. The
First, extraction results of the entire
|Pol.||Linear + circular|
Lastly, we perform NRF extraction on the multiple-aspect-only data at each of the eight polarization states (Case 3: 36 aspects and one polarization states). When
In summary, it is essential to include multiple-aspect data for target characterization because the NRF can be poorly excited at specific transmit-receive configurations [39, 48]. If all the four components in the scattering matrix are utilized for resonance extraction, both linear and circular polarization bases should give similar results. If only one out of the four components in the polarization matrix is utilized (regardless single or multiple aspects), circularly polarized components are preferred over linearly polarized components as some of the dominant modes may not be retrieved in certain linear polarization states. Compared to previous studies that require a large number of target signatures from multiple linear polarization angles (6  and 18 ), the computational load is reduced to the maximum of four or even one without deteriorating the accuracies of the extracted NRF when polarimetric signature is utilized to handle the polarization dependency of the residues. The findings presented here provide us with guidelines on how we should illuminate the targets and process the
3.3. Subsurface target detection
Other than target recognition problems with the target in free space, research activities have also focused on subsurface target detection—where the target is located at a particular depth below an interface. The motivation of subsurface target detection first originated from unexploded ordinance (UXO) detection using ground-penetrating radar [56, 57, 58, 59, 60] and later detection of tumors inside a breast volume [49, 51, 55, 61] as well as detection of small changes in hip prostheses [62, 63, 64].
In the subsurface target detection problem, usually the excitation and the measured field points are located in one medium, and the target is located in another medium. The scattered response is no longer solely dependent on the target itself but also interactions between the target and the interface. These interactions vary as the dielectric contrast between the two media, the depth and the orientation of the target [56, 57, 58, 59, 60], as well as the interactions between the heterogeneity of the medium and the target. In , a transient scattering of metallic targets sited below lossless and lossy half space is studied using joint TF analysis. All the interactions of the target and the dielectric interface, as well as attenuation phenomena due to the non-zero conductivity of the half space, are clearly observed in the joint TF domain. Considering a relatively simple situation where both media are homogeneous, studies have demonstrated that there are two types of resonances associated with the entire scattering problem—a target resonance and an image resonance. A target resonance is the NRF associated with the target attributes (geometry and the dielectric properties) and the dielectric properties of the medium in which the target is embedded [56, 57, 58, 59, 60]. An image resonance is the NRF that corresponds to the target depth—the distance between the target and the interface of the two media [56, 57]. For target detection and recognition applications, the target NRF is of interest. Studies [56, 57, 58, 63] showed that the target NRFs forms a spiral trajectory in the S-plane as the target depth changes. The spiral trajectory surrounds the target NRF within a homogeneous environment—the case where the target is fully immersed in the environment without a dielectric interface.
Other than the characterization of the target resonances for the subsurface target, attempts have also been made to apply the E-pulse for monitoring depth changes [64, 66] and geometrical changes  of a hip prosthesis model sited below a half space of tissue. Results show that the E-pulse technique is capable of detecting both depth changes and physical changes of the target. A subsurface target detection technique is proposed in which the E-pulse is constructed using the NRFs for a target inside a homogenous environment  to approximate the target NRFs for subsurface targets. This E-pulse is convolved with target signatures from the subsurface target and shows that this approximate technique can distinguish between different targets [34, 68, 69].
3.4. Other applications
A critical issue that affects the accuracies of the extracted NRFs is the commencement of the late time or the turn-on time of the resonant modes . The damped exponential model given by Eq. (2) is strictly only valid during the late time period. The early time consists of high-frequency scattering centers that are mainly local scattering events, which can be modeled using the entire functions (e.g., a Gaussian ). The inclusion of the early time period into the NRF extraction process will undoubtedly degrade the accuracies of the retrieved NRFs. Automated detection of the commencement of late time without a priori knowledge of the target geometry or orientation becomes crucial for ATR. Hargrave et al.  proposed a method to estimate the commencement of the late time based on intrinsic differences between the full-rank Hankel matrix generated from the early time data and the rank-deficient late time matrix generated by discrete resonant components. Rezaiesarlak and Manteghi [71, 72] propose the short-time matrix pencil method (STMPM), which mostly applies the MPM for NRF extraction within a time window with a proper direction. The time window is moved by small time steps, and the extraction process is repeated until the entire signal is covered. The STMPM was first applied to chipless radio-frequency identification (RFID) application [71, 72, 73, 74]. Data is encoded as NRFs of the RFID tagged by incorporating notches in the structure such that each RFID tag has different NRFs [73, 74].
In addition to the applications above, the concept of late time resonances has also been applied to sensing applications in other disciplines. This includes monitoring the deployment of arterial stents , nondestructive evaluation of the maturity of fruit , automated detection of objects fallen on railway tracks , nondestructive evaluation of layered materials [78, 79], and detection of concealed handguns .
4. Conclusions and ongoing challenges
The fundamentals and development of resonance-based target recognition over the last 40 years have been briefly reviewed. Prospects of using polarimetric transient signatures for target classification and recognition have been demonstrated through numerical examples. Results show that the use of polarimetric signatures will undoubtedly enhance the ATR performance while reducing the amount of data to process.
Other than using a linear polarization basis to synthesize the circularly polarized target signature, the challenges for designing circularly polarized time-domain antennas  that directly generate circularly polarized pulses are an ongoing research topic for antenna engineers. In situations where the targets under test are very similar, the resonance-based target recognition would perform poorly and probably fails. Recent results in [51, 82, 83] have shown that incorporating polarimetric features, e.g., characteristic polarization states (CPS) of the resonance modes, can solve the problem. Development of novel target recognition schemes that utilize these novel feature sets would be of practical interest to the radar community.
In addition to defense and security applications, recent studies have been looking into the potential of applying the technology to nondestructive evaluations, medical diagnosis, RFID, and agricultural applications. Compared to radar applications where the target is isolated (e.g., aircrafts in the sky) and located in the far-field region and direct signal path from transmitting and receiving antennas exists higher-order interactions between the targets and antennas as well as scattering from surrounding objects become significant especially when the target is located in the near-field region in medical diagnosis [52, 53] and aforementioned RFID applications. Novel calibration procedures [84, 85] and signal processing solutions for NRF extractions of multiple targets [86, 87, 88] are still ongoing research topics for researchers to explore. Regarding subsurface target detection, our results demonstrate that the E-pulse is capable of detecting changes of the NRFs of subsurface targets due to depth [64, 66] and geometrical changes . In conjunction with target NRF, other features embedded in the target signature, such as the “turn-on” time of the resonance , could also be used for these applications. Rather than solely relies on NRF for ATR, the trend of having a “combined” feature set with other parameters (e.g., CPS, turn-on time) will become the fashion for further development in this context.
Sullivan RJ. Radar Foundations for Imaging and Advanced Concepts. Raleigh: Scitech Publishing; 2004
Knott EF, Shaeffer JF, Tuley MT. Radar Cross Section: Its Predication, Measurement and Reduction. Dedham, MA: Artech house; 1985
Copeland JR. Radar target classification by polarization properties. Proceedings of the IRE. 1960; 48:1290-1296
Li HJ, Yang SH. Using range profiles as feature vectors to identify aerospace objects. IEEE Transactions on Antennas and Propagation. 1993; 41:261-268
Hurst M, Mittra R. Scattering center analysis via Prony's method. IEEE Transactions on Antennas and Propagation. 1987; 35:986-988
Lin H, Ksienski AA. Optimum frequencies for aircraft classification. IEEE Transactions on Aerospaces Electronic Systems. 1981; 17:656-665
Baum CE. The singularity expansion method. In: Felsen LB, editor. Transient Electromagnetic Fields. 1st ed. Vol. 10. Berlin; New York: Springer-Verlag; 1976. pp. 129-176
Shuley N, Longstaff D. Role of polarisation in automatic target recognition using resonance descriptions. Electronics Letters. 2004; 40:268-270
Rothwell E, Nyquist D, Chen KM, Drachman B. Radar target discrimination using the extinction-pulse technique. IEEE Transactions on Antennas and Propagation. 1985; 33:929-937
Rothwell E, Chen KM, Nyquist DP, Sun W. Frequency domain E-pulse synthesis and target discrimination. IEEE Transactions on Antennas and Propagation. April, 1987; 35(4):426-434
Ilavarasan P, Ross JE, Rothwell EJ, Chen KM, Nyquist DP. Performance of an automated radar target pulse discrimination scheme using E pulses and S pulses. IEEE Transactions on Antennas and Propagation. May, 1993; 41(5):582-588
Iwaszczuk K, Heiselberg H, Jepsen PU. Terahertz radar cross section measurements. Optics Express. 2010; 18(25):26399-26408. DOI: 10.1364/OE.18.026399
Lui HS, Taimre T, Lim YL, Bertling K, Dean P, Khanna SP, Lachab M, Valavanis A, Indjin D, Linfield EH, Davies AG, Rakic AD. Terahertz radar cross section characterization using self-mixing interferometry with a quantum Cascade laser. Electronics Letters. 22nd Oct. 2015; 51(22):1774-1776
Kennaugh EM, Moffatt DL. Transient and impulse response approximations. Proceedings of the IEEE. 1965; 53:893-901
Heyman E, Felsen L. A wavefront interpretation of the singularity expansion method. IEEE Transactions on Antennas and Propagation. 1985; 33:706-718
Felsen L. Comments on early time SEM. IEEE Transactions on Antennas and Propagation. 1985; 33:118-119
Jang S, Choi W, Sarkar TK, Salazar-Palma M, Kyungjung K, Baum CE. Exploiting early time response using the fractional Fourier transform for analyzing transient radar returns. IEEE Transactions on Antennas and Propagation. 2004; 52:3109-3121
Harrington R. Field computation by the moment method. 2nd ed. USA: IEEE Press; 1993
Van Blaricum M, Mittra R. A technique for extracting the poles and residues of a system directly from its transient response. IEEE Transactions on Antennas and Propagation. 1975; 23:777-781
Sarkar TK, Pereira O. Using the matrix pencil method to estimate the parameters of a sum of complex exponentials. IEEE Antennas and Propagation Magazine. Feb, 1995; 37(1):48-55
Lui HS, Shuley N. On the analysis of electromagnetic transients from radar targets using smooth pseudo Wigner-Ville distribution (SPWVD). Proc. IEEE Antenna Propag. Society Int. Symp., pp. 5701-5704, Honolulu, HI, Jun. 10–15, 2007
Lui HS, Shuley NV. On the modelling of transient scattering under ultra wideband sources. Asia Pacific Symp. Electromag. Compat., Beijing, China. 12–16 April 2010. pp. 854‐857
Rao SM. Time Domain Electromagnetics. San Diego: Academic Press; 1999
FEKO, 32 Techno Lane, Technopark, Stellenbosch, 7600, South Africa: EM Software and System S.A., (pty) Ltd
Rothwell EJ, Chen KM, Nyquist DP. Approximate natural response of an arbitrarily shaped thin wire Scatterer. IEEE Transactions on Antennas Propagation. Oct 1991; 39(10):1457-1462
Cohen L. Time-Frequency Analysis. Englewood Cliffs, NJ: Prentice Hall; 1995
Auger F, Flandrin P, Goncalves P, Lemoine O. Time-Frequency Toolbox – For Use with MATLAB. CNRS (France) and Rice University (USA; 1996)
Lui HS, Shuley NV, Longstaff ID. Time-frequency analysis of late time electromagnetic transients from radar targets. Proc. IET Radar 2007, Pp. 1-5, the Edinburgh International Conference Centre, UK. 15–18 Oct., 2007
Lui HS, Shuley NV. Joint time-frequency analysis on UWB radar signals. Proc. Int.l Conf. Signal Process. Comm. Sys., Gold Coast, Australia, 17–19 Dec. 2007
Lui HS, Shuley NVZ. Evolutions of partial and global resonances in transient electromagnetic scattering. IEEE Antennas on Wireless Propagation Letters. 2008; 7:435-439
Tesche FM. On the analysis of scattering and antenna problems using the singularity expansion technique. IEEE Transactions on Antennas and Propagation. Jan., 1973; 21(1):53-62
Van Blaricum M, Pearson L, Mittra R. An efficient scheme for radar target recognition based on the complex natural resonances of the target. IEEE Antennas and Propagation Society International Symposium. 1975; 13:416-419
Lui HS, Shuley NVZ. Radar target identification using a “banded” E-pulse technique. IEEE Transactions on Antennas and Propagation. Dec., 2006; 54(12):3874-3881
Lui HS, Shuley NVZ, Rakic AD. A novel, fast, approximate target detection technique for metallic target below a frequency dependent Lossy Halfspace. IEEE Transactions on Antennas and Propagation. May 2010; 58(5):1699-1710
Lui HS, Shuley NVZ. Sampling procedures in resonance based radar target identification. IEEE Transactions on Antennas and Propagation. May 2008; 56(5):1487-1491
Rothwell E, Kun-Mu C, Nyquist D. Extraction of the natural frequencies of a radar target from a measured response using E-pulse techniques. IEEE Transactions on Antennas and Propagation. 1987; 35:715-720
Gallego A, Medouri A, Carmen Carrion M. Estimation of number of natural resonances of transient signal using E-pulse technique. Electronics Letters. 1991; 27:2253-2256
Ruiz DP, Carrion MC, Gallego A, Medouri A. Parameter estimation of exponentially damped sinusoids using a higher order correlation-based approach. IEEE Transactions on Signal Processing. Nov. 1995; 43(11):2665-2677
Sarkar TK, Park S, Koh J, Rao SM. Application of the matrix pencil method for estimating the SEM (singularity expansion method ) poles of source-free transient responses from multiple look directions. IEEE Transactions on Antennas and Propagation. April, 2000; 48(4):612-618
Kennaugh E. The K-pulse concept. IEEE Transactions on Antennas and Propagation. 1981; 29:327-331
Chen KM, Nyquist D, Rothwell E, Webb L, Drachman B. Radar target discrimination by convolution of radar return with extinction-pulses and single-mode extraction signals. IEEE Transactions on Antennas and Propagation. 1986; 34:896-904
Rothwell EJ, Chen KM. A hybrid E-pulse/least squares technique for natural resonance extraction. Proceedings of the IEEE. 1988; 76:296-298
Carrion MC, Gallego A, Porti J, Ruiz DP. Subsectional-polynomial E-pulse synthesis and application to radar target discrimination. IEEE Transactions on Antennas and Propagation. 1993; 41:1204-1211
Blanco D, Ruiz DP, Alameda E, Carrion MC. An asymptotically unbiased E-pulse-based scheme for radar target discrimination. IEEE Transactions on Antennas and Propagation. 2004; 52:1348-1350
Lui HS, Shuley N. Resonance Based Radar Target Detection with Multiple Polarisations. Proc. IEEE Antennas Propag. Soc. Int. Symp. USNC/URSI National Radio Science Meeting. 9–14 July, 2006, Albuquerque, New Mexico, USA. pp. 3259-3262
Mott H. Remote Sensing with Polarimetric Radar. New Jersey: Wiley; 2007
Lui HS, Shuley NVZ. Resonance based target recognition using ultra-wideband Polarimetric signatures. IEEE Transactions on Antennas and Propagation, New Jersey. August 2012; 60(8):3985-3988
Zhang H, Fan Z, Ding D, Chen R. Radar target recognition based on multi-directional E-pulse technique. IEEE Transactions on Antennas and Propagation. Nov. 2013; 61(11):5838-5843
Lui HS. Characterization of radar target using multiple transient responses. IEEE Antennas on Wireless Propagation Letters. Sept. 2015; 14:1750-1753
Lui HS, Fhager A, Persson M. On the forward scattering of microwave breast imaging. International Journal of Biomedical Imaging, 15 Pages. May 2012
Lui HS, Fhager A, Yang J, Persson M. Characterization and detection of breast cancer using ultra wideband Polarimetric transients. European Conference on Antennas and Propagation. Gothenburg, Sweden, 8–11 April 2013. pp. 2909‐2913
Lui HS, Fhager A, Persson M. Preliminary Investigations of Three-Dimensional Microwave Tomography Using Different Data Sets. European Conference on Antennas and Propagation, Prague, Czech Republic. 26–30 March 2012
Lui HS, Fhager A, Persson M. Antenna Configurations of Microwave Breast Imaging. Asia Pacific Microwave Conference, 5–8 Nov., 2013, Seoul, Korea
Gabriel S, Lau RW, Gabriel C. The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. Physics in Medicine and Biology. Nov. 1996; 41(11):2271-2293
Huo Y, Bansal R, Zhu Q. Modeling of noninvasive microwave characterization of breast tumors. IEEE Transactions on Biomedical Engineering. 2004; 51:1089-1094
Vitebskiy S, Carin L. Moment-method modeling of short-pulse scattering from and the resonances of a wire buried inside a lossy, dispersive half-space. IEEE Transactions on Antennas and Propagation. 1995; 43:1303-1312
Geng N, Jackson DR, Carin L. On the resonances of a dielectric BOR buried in a dispersive layered medium. IEEE Transactions on Antennas and Propagation. 1999; 47:1305-1313
Wang Y, Longstaff ID, Leat CJ, Shuley NV. Complex natural resonances of conducting planar objects buried in a dielectric half-space. IEEE Transactions on Geoscience Remote Sensing. 2001; 39:1183-1189
Chen C-C, Peters L Jr. Buried unexploded ordnance identification via complex natural resonances. IEEE Transactions on Antennas and Propagation. 1997; 45:1645-1654
Baum CE. Detection and Identification of Visually Obscured Targets. Philadelphia: Taylor & Francis; 1999
Lui HS, Li BK, Shuley N, Crozier S. Preliminary Investigation of Breast Tumor Detection Using the E-Pulse Technique. Proc. IEEE Antenna Propag. Soc. Int. Symp. USNC/URSI National Radio Science Meeting, pp. 283-286, 9–14 July. 2006. Albuquerque, New Mexico, USA
Lui HS, Shuley N, Crozier S. A Concept for Hip Prosthesis Identification Using Ultra Wideband Radar. Proc. 26th Annual Int. Conf. of the IEEE Engineering in Medicine and Biology Society. pp. 1439‐1442, 1–5 Sept. 2004, San Francisco, CA, USA
Lui HS, Shuley N, Crozier S. Hip Prosthesis Detection Based on Complex Natural Resonances. Proc. 27th Annual Int.l Conf. of the IEEE Engineering in Medicine and Biology Society, 1–5 Sept. 2005. Shanghai, China. pp. 1571‐1574
Lui HS, Shuley N, Padhi SK, Crozier S. Detection of hip prosthesis depth changes using an E-pulse technique. Topical Meeting on Biomedical Electromagnetics. 17th International Zurich Symposium on Electromagnetic Compatibility. 27 February to 3 march 2006, Singapore. pp. 81-84
Lui HS, Shuley N, Persson M. Joint time-frequency analysis of transient electromagnetic scattering from a subsurface target. IEEE Antennas and Propagation Magazine. Oct. 2012; 54(5):109-130
Lui HS, Shuley NVZ. Detection of depth changes of a metallic target buried inside a Lossy Halfspace using the E-pulse technique. IEEE Transactions on Electromagnetic Compatibility. November 2007; 49(4):868-875
Lui HS, Aldhubaib F, Shuley NVZ, Hui HT. Subsurface target recognition based on transient electromagnetic scattering. IEEE Transactions on Antennas and Propagation. October 2009; 57(10):3398-3401
Lui HS, Shuley N. Subsurface target recognition using an approximated method. Asia Pacific Microw. Conf. Singapore, 7–10 Dec. 2009. pp. 2216-2219
Lui HS, Shuley NV. Performance evaluation of subsurface target recognition based on ultra-wideband short pulse excitation. IEEE Int. Symp. Antennas Propag., pp. 1‐4, Toronto, Ontario, Canada, July 11–17, 2010
Hargrave CO, Clarkson IVL, Lui HS. Late-time estimation for resonance-based radar target identification. IEEE Transactions on Antennas and Propagation. Nov., 2014; 62(11):5865-5871
Rezaiesarlak R, Manteghi M. Short-time matrix pencil method for Chipless RFID detection applications. IEEE Transactions on Antennas Propagation. May 2013; 61(5):2801-2806
Rezaiesarlak R, Manteghi M. On the application of short-time matrix pencil method for wideband scattering from resonant structures. IEEE Transactions on Antennas Propagation. Jan. 2015; 63(1):328-335
Blischak AT, Manteghi M. Embedded singularity Chipless RFID tags. IEEE Transactions on Antennas Propagation. Nov 2011; 59(11):3961-3968
Rezaiesarlak R, Manteghi M. Complex-natural-resonance-based Design of Chipless RFID tag for high-density data. IEEE Transactions on Antennas Propagation. Feb 2014; 62(2):898-904
Manteghi M, Cooperand DB, Vlachos PP. Application of singularity expansion method for monitoring the deployment of arterial stents. Microwave and Optical Technology Letters. 2012; 54(10):2241-2246
Tantisopharak T, Moon H, Youryon P, Bunya-Athichart K, Krairiksh M, Sarkar TK. Nondestructive determination of the maturity of the durian fruit in the frequency domain using the change in the natural frequency. IEEE Transactions on Antennas Propagation. Feb 2016; 64(5):1779-1787
Mroué A, Heddebaut M, Elbahhar F, Rivenq A, Rouvaen J-M. Automatic radar target recognition of objects falling on railway tracks. Measurement Science and Technology. Jan. 2012; 23(2). DOI: 10.1088/0957-0233/23/2/025401
Stenholm G, Rothwell EJ, Nyquist DP, Kempel LC, Frasch LL. E-pulse diagnostics of simple layered materials. IEEE Transactions on Antennas and Propagation. Dec. 2003; 51(12):3221-3227
Wierzba JF, Rothwell EJ. E-pulse diagnostics of curved coated conductors with varying thickness and curvature. IEEE Transactions on Antennas and Propagation. September 2006; 54(9):2672-2676
Harmer SW, Andrews DA, Rezgui ND, Bowring NJ. Detection of handguns by their complex natural resonant frequencies. IET Microwaves, Antennas and Propagation. 2010, 2010; 4(9):1182-1190. DOI: 10.1049/iet-map.2009.0382
Shlivinski A. Time domain circularly polarized antenna. IEEE Transactions on Antennas and Propagation. June 2009; 57(6):1606-1611
Aldhubaib F, Shuley NVZ, Lui HS. Characteristic polarization states in an ultra-wide-band context based on singularity expansion method. IEEE Geoscience and Remote Sensing Letters. Oct. 2009; 6(4):792-796
Lui HS, Persson M. Characterization of radar targets based on ultra wideband Polarimetric transient signatures. XXX URSI General Assembly and Scientific Symposium of International Union of Radio Science. pp. 1‐4. Istanbul, Turkey. 13–20 Aug. 2011
Sarkar TK, Tseng FI, Rao SM, Dianat SA, Hollmann BZ. Deconvolution of impulse response from time-limited input and output: Theory and experiment. IEEE Transactions on Instrumentation and Measurement. 1985; 34:541-546
Bannawata L, Boonpoongaa A, Burintramartb S, Akkaraekthalina P. On the resolution improvement of radar target identification with filtering antenna effects. International Journal of Antennas Propagation. accepted for publication, Dec 2017
Rezaiesarlak R, Manteghi M. A space–time–frequency Anticollision algorithm for identifying chipless RFID. IEEE Transactions on Antennas Propagation. Mar 2014; 62(3):1425-1432
Lee W, Sarkar TK, Moon H, Salazar-Palma M. Identification of multiple objects using their natural resonant frequencies. IEEE Antennas and Wireless Propagation Letters. 2013; 12:54-57
Lee JH, Jeong SH, Park GS, Lee YC, Cho SW. Performance analysis of natural frequency-based multiple radar target recognition for multiple-input–multiple-output radar application. IET Radar, Sonar and Navigation. June 2014; 8(5):457-464